Quantum computation aims at manipulating delicate entangled states to achieve functionalities beyond those presented by classical devices. Robust large-scale quantum computers will likely require quantum error-correction (QEC) to exploit the wide range of applications offered by a universal quantum processor [1]}. In particular, scalable quantum error correction codes (QECCs) preserve quantum information by encoding it redundantly in a set of physical qubits [1]} such that, in principle, arbitrary levels of protection can be achieved by increasing the number of redundant physical qubits while employing active detection and correction of errors, provided physical noise rates lie below the critical threshold of the corresponding QECC. Together with a fault-tolerant methodology [3]}, which forbids the uncontrolled proliferation of errors by the specific design of the scalable QEC circuits, this yields one of the most promising approaches towards large-scale quantum computation. However, to achieve the required levels of protection, there are experimental and theoretical challenges that need to be addressed. In particular, identifying and mitigating noise sources so that minimal QECCs are shown to outperform their physical/bare counterparts is considered a break-even point in the road-map for realising QEC for large-scale quantum computers [4]}, [5]}.
